Triggered by the discovery of high-transition-temperature (high-Tc) superconducting copper oxides in 1986, eight different material families have been found to show superconductivity at temperatures higher than 23 K, the record high-Tc value before 1986. Among them six families are superconductors with Tcmax lower than 40 K, and the electron-electron attractive interaction mediated by phonons is thought to be a dominant pairing interaction. The copper oxides and the iron compounds are distinct from others in their outstandingly high Tc values, 135 K and 55 K, respectively, and in unconventional Cooper pairs, supposedly arising from repulsive interactions. 　Although the mechanisms of Cooper pair formation in both systems remain to be elucidateddeb, now we can specify material parameters that influence Tc in each family.

　Most of them do not obey the Matthias rules which were a guiding principle for finding new superconducting materials with high Tc before 1986. Instead, new guiding principles emerge from the features in common with most of these high-Tc families. This lecture addresses the basic questions; what makes Tc high in each family and why copper oxides and iron compounds are so special with central concern on a possibility of enhancing Tc